% !TeX root =main.tex
\begin{table}[h]
	\caption{Number of trees per species in dataset \#1; measured ranges of tree circumference (C130), height and total volume (Vtot). Species common to dataset \#1 and \#2 are highlighted in gray.}
	\bigskip
	\centering
	\small
		\begin{tabular}{llccccc}
			\hline
			Genus & Species & Number & $C130$ range	& Height range	& $Vtot$ range \\
			           &               & of trees & (cm)		& (m)		& (m$^3$) \\
			\hline
		% début auto
			\multicolumn{6}{c}{Angiosperms}\\
			\rowcolor[gray]{0.9}
			\textit{Betula} & \textit{pendula} & 16 & $ 37- 98$ & $14.7 - 28.5$ & $0.08 - 1.02$ \\
			\rowcolor[gray]{0.9}
			\textit{Carpinus} & \textit{betulus} & 77 & $ 24-120$ & $11.3 - 30.0$ & $0.03 - 2.38$ \\
			\rowcolor[gray]{0.9}
			\textit{Fagus} & \textit{sylvatica} & 1987 & $ 22-249$ & $ 5.5 - 42.5$ & $0.01 - 7.46$ \\
			\rowcolor[gray]{0.9}
			\textit{Fraxinus} & \textit{excelsior} & 115 & $ 26-136$ & $11.5 - 26.7$ & $0.04 - 2.47$ \\
			\textit{Quercus} & \textit{palustris} & 24 & $ 22- 74$ & $ 8.9 - 16.5$ & $0.02 - 0.44$ \\
			\rowcolor[gray]{0.9}
			\textit{Quercus} & \textit{petraea/robur} & 1748 & $ 22-320$ & $ 6.0 - 40.0$ & $0.02 - 18.12$ \\
			\textit{Quercus} & \textit{rubra} & 110 & $ 22-109$ & $10.9 - 23.5$ & $0.03 - 0.96$ \\
			\hline
			\multicolumn{6}{c}{Gymnosperms}\\
			\textit{Abies} & \textit{alba} & 1095 & $ 22-283$ & $ 6.9 - 37.8$ & $0.02 - 10.25$ \\
			\textit{Abies} & \textit{nordmanniana} & 40 & $ 22-119$ & $ 3.5 - 27.0$ & $0.02 - 1.62$ \\
			\textit{Larix} & \textit{decidua} & 92 & $ 29-134$ & $ 9.0 - 25.6$ & $0.04 - 1.95$ \\
			\textit{Picea} & \textit{abies} & 318 & $ 24-210$ & $ 7.7 - 41.3$ & $0.02 - 6.59$ \\
			\textit{Picea} & \textit{sitchensis} & 12 & $ 28- 44$ & $ 9.5 - 14.0$ & $0.04 - 0.14$ \\
			\textit{Pinus} & \textit{laricio} & 158 & $ 40-160$ & $13.3 - 33.4$ & $0.08 - 3.68$ \\
			\textit{Pinus} & \textit{nigra} & 23 & $ 31-109$ & $ 8.9 - 27.0$ & $0.04 - 1.28$ \\
			\textit{Pinus} & \textit{pinaster} & 777 & $ 22-139$ & $ 5.1 - 23.5$ & $0.01 - 1.70$ \\
			\textit{Pinus} & \textit{strobus} & 32 & $ 25-114$ & $ 7.9 - 25.0$ & $0.03 - 1.34$ \\
			\textit{Pinus} & \textit{sylvestris} & 1012 & $ 22-223$ & $ 9.4 - 29.3$ & $0.02 - 7.70$ \\
			\textit{Pinus} & \textit{uncinata} & 166 & $ 26-127$ & $ 6.7 - 20.5$ & $0.03 - 1.65$ \\
			\textit{Pseudotsuga} & \textit{menziesii} & 390 & $ 22-107$ & $ 7.0 - 29.5$ & $0.02 - 1.12$ \\
			\hline
			Total & 19 species & 8192 & $ 22-320$ & $ 3.5 - 42.5$ & $0.01 - 18.12$ \\
			\hline
		% fin auto

		\end{tabular}
	\label{tableEssences1}
\end{table}

\begin{table}[h]
	\caption{Number of trees per species in dataset \#2; measured ranges of tree circumference ($C130$), height and total volume (Vtot). Species common to dataset \#1 and \#2 are highlighted in gray.}
	\bigskip
	\centering
	\small
		\begin{tabular}{llccccc}
			\hline
			Genus & Species & Number & $C130$ range	& Height range	& $Vtot$ range \\
			           &               & of trees & (cm)		& (m)		& (m$^3$) \\
			\hline
		% début auto
			\multicolumn{6}{c}{Angiosperms}\\
			\textit{Acer} & \textit{pseudoplatanus} & 23 & $ 38-136$ & $16.3 - 22.9$ & $0.10 - 2.15$ \\
			\rowcolor[gray]{0.9}
			\textit{Betula} & \textit{pendula} & 13 & $ 32-164$ & $10.1 - 28.9$ & $0.04 - 3.94$ \\
			\rowcolor[gray]{0.9}
			\textit{Carpinus} & \textit{betulus} & 2 & $ 59- 93$ & $18.2 - 22.9$ & $0.30 - 1.04$ \\
			\rowcolor[gray]{0.9}
			\textit{Fagus} & \textit{sylvatica} & 34 & $ 35-240$ & $16.8 - 27.1$ & $0.08 - 10.72$ \\
			\rowcolor[gray]{0.9}
			\textit{Fraxinus} & \textit{excelsior} & 8 & $ 83-204$ & $20.6 - 29.9$ & $0.74 - 7.36$ \\
			\textit{Populus} & \textit{tremula} & 2 & $ 70- 94$ & $21.8 - 25.9$ & $0.58 - 0.95$ \\
			\textit{Quercus} & \textit{ilex} & 23 & $ 22- 62$ & $ 4.2 - 10.4$ & $0.01 - 0.22$ \\
			\rowcolor[gray]{0.9}
			\textit{Quercus} & \textit{petraea/robur} & 24 & $ 56-295$ & $16.2 - 32.8$ & $0.20 - 13.04$ \\
			\textit{Quercus} & \textit{pubescens} & 8 & $ 68-145$ & $16.5 - 20.4$ & $0.46 - 2.01$ \\
			\textit{Alnus} & \textit{sp.} & 16 & $ 75-152$ & $17.7 - 28.0$ & $0.57 - 2.95$ \\
			\textit{Robinia} & \textit{pseudoacacia} & 8 & $ 47- 76$ & $20.1 - 23.5$ & $0.19 - 0.55$ \\
			\textit{Tilia} & \textit{sp.} & 7 & $ 67-136$ & $22.9 - 25.1$ & $0.54 - 2.89$ \\
			\hline
			\multicolumn{6}{c}{Gymnosperms}\\
			\textit{Pinus} & \textit{halepensis} & 8 & $ 56-201$ & $10.9 - 17.7$ & $0.17 - 3.52$ \\
			\hline
			Total & 13 species & 176 & $ 22-295$ & $ 4.2 - 32.8$ & $0.01 - 13.04$ \\
			\hline
		% fin auto

		\end{tabular}
	\label{tableEssences2}
\end{table}

\bigskip


\begin{table}[h]
	\caption{RMSE and relative RMSE (in brackets) for $VEF$ and $Vtot$ computed by circumference classes (model corresponding to Equation \eqref{equa7} fitted on the whole calibration dataset \#1).}
	\bigskip
	\centering 
	\scriptsize
		\begin{tabular}{lccccc}
			\hline
			Circumference (cm) & [22-50[ & $\left[50-75\right[$ & $\left[75-100\right[$ & $\left[100-125\right[$ & $\geq125$ \\
			\hline			
			n & 2828 & 2467 & 1467 & 688 & 742 \\	
			RMSE of $VEF$ & 0.165 (12.4\%) & 0.086 (7.5\%) & 0.109 (9.5\%) & 0.138 (11.6 \%) & 0.184 (14.6 \%) \\
			RMSE of $Vtot$ (m$^{3}$) & 0.009 (9.6\%) & 0.024 (7.4 \%) & 0.065 (8.6 \%) & 0.149 (10.2 \%) & 0.469 (13.7 \%) \\ 
			\hline
		\end{tabular}
	\label{table_RMSE_vs_diameter_class}
\end{table}


\begin{table}[h]
	\caption{Parameter estimates by genus based on BLUP computation in the model corresponding to Equation \eqref{equa7} fitted on the whole dataset \#1. Parameter $\beta_{3}'$ for gymnosperms is written in gray since it does not play any role in the model due to the multiplication by $G=0$.}
	\bigskip
	\centering 
	\scriptsize
		\begin{tabular}{lccccccc}
			\hline
			&&&&&& RMSE & RMSE \\
			Genus & $n$ & $\beta_{1}$ & $\beta_{2}+b_{2i}$ & $\beta_{3}'$ & $\beta_{4}+b_{4i}$ & of & of \\
			&&&&&& $VEF$ & $Vtot$ (m$^{3}$) \\
			\hline
			\multicolumn{8}{c}{Angiosperms} \\
			\textit{Betula} & 16 & 21.447 & 0.325 & 1.016 & -0.700 & 0.041 & 0.022  \\	
			\textit{Carpinus} & 77 & 21.447 & 0.361 & 1.016 & -0.326 & 0.146 & 0.099 \\
			\textit{Fagus} & 1987 & 21.447 & 0.270 & 1.016 & -0.517 & 0.200 & 0.200 \\
			\textit{Fraxinus} & 115 & 21.447 & 0.356 & 1.016 & -0.671 & 0.142 & 0.101 \\	
			\textit{Quercus} & 1882 & 21.447 & 0.422 & 1.016 & -0.898 & 0.138 & 0.223 \\
			\hline
			\multicolumn{8}{c}{Gymnosperms} \\
			\textit{Abies} & 1135 & 21.447 & 0.479 & \textcolor{gray}{1.016} & -0.580 & 0.086 & 0.077 \\
			\textit{Larix} & 92 & 21.447 & 0.309 & \textcolor{gray}{1.016} & -0.688 & 0.042 & 0.013 \\
			\textit{Picea} & 330 & 21.447 & 0.303 & \textcolor{gray}{1.016} & -0.671 & 0.039 & 0.048 \\
			\textit{Pinus} & 2168 & 21.447 & 0.180 & \textcolor{gray}{1.016} & -0.811 & 0.096 & 0.042 \\
			\textit{Pseudotsuga} & 390 & 21.447 & 0.236 & \textcolor{gray}{1.016} & -0.364 & 0.088 & 0.023 \\			
			\hline	
		\end{tabular}
	\label{tableMixedModel}
\end{table}

\bigskip
\begin{sidewaystable}[h]
	\caption{Validation of the model on the independent dataset \#2.}
	\bigskip
	\renewcommand{\arraystretch}{0.75}
	\centering 
		\begin{tabular}{llccccc}
			\hline
			&  &  & \multicolumn{2}{c}{Fixed part of the model} & \multicolumn{2}{c}{With species specific coefficients} \\
			Genus & Species & Number of trees & RMSE of the & RMSE of & RMSE of & RMSE of \\
			& & & $VEF$ & $Vtot$ (m$^{3}$) & $VEF$ & $Vtot$ (m$^{3}$) \\
			\hline
			\multicolumn{7}{c}{Tree species used for the model calibration} \\
			\textit{Betula} & \textit{pendula} & 13 & 0.136 & 0.266 & 0.143 & 0.282 \\
			\textit{Carpinus} & \textit{betulus} & 2 & 0.161 & 0.106 & 0.152 & 0.068 \\
			\textit{Fagus} & \textit{sylvatica} & 34 & 0.167 & 0.550 & 0.149 & 0.481 \\			
			\textit{Fraxinus} & \textit{excelsior} & 8 & 0.365 & 1.087 & 0.376 & 1.120 \\
			\textit{Quercus} & \textit{petraea/robur} & 24 & 0.213 & 0.745 & 0.248 & 0.944 \\
			\hline
			\multicolumn{7}{c}{Tree species not used for the model calibration} \\
			\textit{Acer} & \textit{pseudoplatanus} & 23 & 0.130 & 0.098 & - & - \\
			\textit{Alnus} & \textit{sp.} & 16 & 0.161 & 0.217 & - & - \\
			\textit{Pinus} & \textit{halepensis} & 8 & 0.157 & 0.178 & 0.203 & 0.236 \\
			\textit{Populus} & \textit{tremula} & 2 & 0.102 & 0.063 & - & - \\
			\textit{Quercus} & \textit{ilex} & 23 & 1.139 & 0.048 & 0.740 & 0.032 \\
			\textit{Quercus} & \textit{pubescens} & 8 & 0.243 & 0.193 & 0.282 & 0.225 \\
			\textit{Robinia} & \textit{pseudoacacia} & 8 & 0.084 & 0.031 & - & - \\
			\textit{Tilia} & \textit{cordata} & 7 & 0.198 & 0.276 & - & - \\						
			\hline
		\end{tabular}
	\label{RMSE_validation}
\end{sidewaystable}

